According to Long Term Evolution (LTE) standards a base station (eNodeB) may transmit channel state information-reference signals (CSI-RS), or cell-specific reference signals (C-RS) reference signals, to a user equipment (UE, e.g. a cellular telephone or other device) and request the UE to estimate a preferred set of transmission (TX) parameters. The set of TX parameters may include for example:                RI—MIMO rank indication, which indicates the number of layers that should be used for downlink (DL) transmission to the UE.        PMI—pre-coder matrix indication.        CQI—channel quality indication that defines the constellation, e.g., quadrature phase-shift keying (QPSK), 16 Quadrature amplitude modulation (QAM), 64 QAM and 256 QAM, and code rate.        
The UE may report to the base station a TX parameters vector, e.g., [RI, PMI, CQI] that may maximize DL capacity under a required block error rate (BLER).
In order to choose the best suitable set of TX parameters, a UE should have precise evaluation of the expected link performance under current channel conditions. The UE should report TX parameters that are suitable for high downlink rate transmission. However, the UE must not report TX parameters combination that has block error rate (BLER) above a predefined level, e.g., 0.1. According to the LTE standard, a transport block is divided into smaller size code blocks. BLER may refer to a ratio or portion of the average number of erroneous code-blocks out of total transmitted code-blocks. For example, the UE may report TX parameters that provide the highest downlink rate transmission with BLER equal to or below 0.1.
The process of TX parameters estimation may include estimating the effective channel, Heff based on reference signals received from the base station, e.g., CSI-RS (or C-RS), estimating the mutual information per bit (MIB) or the effective signal-to-noise ratio (SNR), SNReff, and estimating the expected BLER based on the MIB or SNReff, for every combination of [RI, PMI, CQI]. The best combination of [RI, PMI, CQI] may be reported to the base station. Mean MIB (MMIB) or effective exponential SNR mapping (EESM) may be seen as metrics that abstract channel conditions and noise.
Known methods for selecting TX parameters, commonly referred to as EESM, may include estimating effective SNR, SNReff, by averaging post-processing SNR (PP-SNR) over all subcarriers, for example according to:
                              SNR          eff                =                              -            β                    ·                      ln            ⁡                          (                                                1                  N                                ⁢                                                      ∑                                          k                      =                      1                                        N                                    ⁢                                      e                                          -                                                                        γ                          k                                                β                                                                                                        )                                                          (                  Equation          ⁢                                          ⁢          1                )            Where N is the number of sub carriers, γk is the effective SNR of kth subcarrier and β is a parameter calibrated for every code rate and every block size. EESM may predict the performance of a linear MIMO decoder e.g. minimum mean square error (MMSE) or zero-forcing (ZF) decoders accurately, by feeding PP-SNR into γk. PP-SNR may refer to the signal to noise and interference ratio after equalizing MIMO interferences. However, when maximum likelihood decoding (MLD) is used, PP-SNR has no analytic closed form expression or convenient approximation and thus is not known. Using PP-SNR of a linear MIMO decoder (e.g., MMSE or ZF) for predicting MLD performance provides poor results. Thus, for MLD, EESM yields poor prediction of link performance, e.g., of BLER.
According to a second method, given bit log-likelihood ratios (LLRs), outputs of MLD, MIB may be calculated according to:
                    MIB        =                              I            ⁡                          (                              b                ;                LLR                            )                                =                                    ∑                              b                ∈                                  {                                      0                    ,                    1                                    }                                                      ⁢                                          ∫                                  -                  ∞                                ∞                            ⁢                                                P                  ⁡                                      (                                          LLR                      ,                      b                                        )                                                  ⁢                                                      log                    2                                    ⁡                                      (                                                                  P                        ⁡                                                  (                                                      LLR                            ,                            b                                                    )                                                                                                                      P                          ⁡                                                      (                            LLR                            )                                                                          ⁢                                                  P                          ⁡                                                      (                            b                            )                                                                                                                )                                                  ⁢                dLLR                                                                        (                  Equation          ⁢                                          ⁢          2                )            In equation 2, MIB measures the amount of information that the LLRs provide on each bit. Mean MIB (MMIB) is a measure of average MIB values over all constellation bits and over all subcarriers that are received from the current channel. MIB may be averaged over all subcarriers using an arithmetic (simple) averaging:
                    MMIB        =                              1            N                    ⁢                                    ∑                              k                =                1                            N                        ⁢                          MIB              k                                                          (                  Equation          ⁢                                          ⁢          3                )            Where MIBk is the MIB of kth subcarrier and N is the number of subcarriers.
According to Gaussian mixture model (GMM), it may be assumed that the distribution function of LLRs may be a mixture of Gaussians. For single input single output (SISO) channel and quadrature phase-shift keying (BPSK) modulation, MIB may be represented by:
                    MIB        =                  J          ⁡                      (                                          8                ⁢                                                      E                    s                                                        N                    0                                                                        )                                              (                  Equation          ⁢                                          ⁢          4                )                                where        ⁢                  :                                                                              j          ⁡                      (            σ            )                          =                  1          -                                    ∫                              -                ∞                            ∞                        ⁢                                          1                                                                            2                      ⁢                      π                                                        ⁢                  σ                                            ⁢                                                e                                      -                                                                                            (                                                      z                            -                                                                                          σ                                2                                                            /                              2                                                                                )                                                2                                                                    σ                        2                                                                                            ·                log                            ⁢                              (                                  1                  +                                      e                                          -                      z                                                                      )                            ⁢              dz                                                          (                  Equation          ⁢                                          ⁢          5                )            For higher constellations and MIMO channels, LLRs may be approximated by a mixture of several Gaussians and MIB may be represented by:MIB=c1*J(a√{square root over (γ1)})+c2*J(b√{square root over (γ2)})+c3*J(c√{square root over (γ3)})  (Equation 6)Where c1, c2 and c3 are coefficients that depend on the constellation. γ1, γ2 and γ3 are derived from Eigen values of the channel matrix and a, b and c are pre-calibrated coefficients. However, the GMM model is difficult to calibrate and achieves poor performance when applied to MIMO channels with high correlation between MIMO layers.
Thus, an efficient method for calculating MIB for MIMO channels is required.